Stability and Hopf bifurcation of HIV-1 model with Holling II infection rate and immune delay
作者：
Liao, Maoxin;Liu, Yanjin* ;Liu, Shinan;Meyad, Ali M.
期刊：
Journal of Biological Dynamics ,2022年16(1):397-411 ISSN：1751-3758
通讯作者：
Liu, Yanjin
作者机构：
[Liu, Shinan; Liao, Maoxin; Liu, Yanjin] Univ South China, Sch Math & Phys, Hengyang, Peoples R China.;[Meyad, Ali M.] Southwestern Univ Finance & Econ, Sch Publ Finance & Taxat, Chengdu, Peoples R China.
通讯机构：
[Liu, Yanjin] U;Univ South China, Sch Math & Phys, Hengyang, Peoples R China.
关键词：
34K20;34K60;92B05;92D30;HIV-1 model;Hopf bifurcation;Stability;immune delay
摘要：
This paper aims to analyse stability and Hopf bifurcation of the HIV-1 model with immune delay under the functional response of the Holling II type. The global stability analysis has been considered by Lyapunov–LaSalle theorem. And stability and the sufficient condition for the existence of Hopf Bifurcation of the infected equilibrium of the HIV-1 model with immune response are also studied. Some numerical simulations verify the above results. Finally, we propose a novel three dimension system to the future study. © 2021 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.
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BIFURCATION PROPERTIES FOR FRACTIONAL ORDER DELAYED BAM NEURAL NETWORKS
作者：
Xu, Changjin* ;Liao, Maoxin;Li, Peiluan;Guo, Ying;Liu, Zixin
期刊：
Cognitive Computation ,2021年13(2):322-356 ISSN：1866-9956
通讯作者：
Xu, Changjin
作者机构：
[Xu, Changjin] Guizhou Univ Finance & Econ, Guizhou Key Lab Econ Syst Simulat, Guiyang 550004, Peoples R China.;[Liao, Maoxin] Univ South China, Sch Math & Phys, Hengyang 421001, Peoples R China.;[Li, Peiluan] Henan Univ Sci & Technol, Sch Math & Stat, Luoyang 471023, Peoples R China.;[Guo, Ying] Cent South Univ, Sch Automat, Changsha 410083, Peoples R China.;[Liu, Zixin] Guizhou Univ Finance & Econ, Sch Math & Stat, Guiyang 550004, Peoples R China.
通讯机构：
[Xu, Changjin] G;Guizhou Univ Finance & Econ, Guizhou Key Lab Econ Syst Simulat, Guiyang 550004, Peoples R China.
关键词：
BAM neural networks;Stability;Hopf bifurcation;Fractional order;Delay;Leakage delay
摘要：
In the past several decades, many papers involving the stability and Hopf bifurcation of delayed neural networks have been published. However, the results on the stability and Hopf bifurcation for fractional order neural networks with delays and fractional order neural networks with leakage delays are very rare. This paper is concerned with the stability and the existence of Hopf bifurcation of fractional order BAM neural networks with or without leakage delay. The Laplace transform, stability and bifurcation theory of fractional-order differential equations and Matlab software will be applied. The stability condition and the sufficient criterion of existence of Hopf bifurcation for fractional order BAM neural networks with delay (leakage delay) are established. It is found that when the sum of two delays (leakage delay) crosses a critical value, then a Hopf bifurcation will appear. The obtained results play an important role in designing neural networks. Also the derived results are new and enrich the bifurcation theory of fractional order delayed differential equations. © 2021, Springer Science+Business Media, LLC, part of Springer Nature.
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英文
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一类具有时滞的非线性物价模型的稳定性与Hopf分支
作者：
廖茂新;邓兴颖;张露露
期刊：
南华大学学报(自然科学版) ,2021年35(01):52-55 ISSN：1673-0062
作者机构：
南华大学 数理学院,中国 衡阳421001;[邓兴颖; 张露露; 廖茂新] 南华大学
关键词：
HOPF分支;稳定性;时滞;物价模型
摘要：
结合市场经济实际情况,对一类关于物价的非线性微分方程模型进行了修正,并研究了时滞对该模型动力学行为的影响。利用泛函微分方程稳定性理论和HOPF分支理论得到正平衡点局部稳定的条件,给出了出现HOPF分支存在的充分条件,并通过数值模拟,验证理论分析的结果。
语种：
中文
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一类具有时滞的传染病模型Hopf分支及稳定性分析
作者：
张露露;廖茂新;邓兴颖
期刊：
南华大学学报(自然科学版) ,2021年35(01):71-76 ISSN：1673-0062
作者机构：
南华大学 数理学院,湖南 衡阳421000;[邓兴颖; 张露露; 廖茂新] 南华大学
关键词：
Hopf分支;时滞;平衡点;稳定性
摘要：
研究了一类具有非线性传染率的传染病模型,确定了模型的基本再生数R0,分析了模型无病平衡点和地方病平衡点的稳定性,以时滞为参数,得到了在地方病平衡点处Hopf分支存在的条件、最后数值模拟以验证结果。
语种：
中文
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Impact of leakage delay on bifurcation in fractional-order complex-valued neural networks
作者：
Xu, Changjin;Liao, Maoxin;Li, Peiluan;Yuan, Shuai
期刊：
CHAOS SOLITONS & FRACTALS ,2021年142:110535 ISSN：0960-0779
通讯作者：
Changjin Xu
作者机构：
[Xu, Changjin] Guizhou Univ Finance & Econ, Guizhou Key Lab Econ Syst Simulat, Guiyang 550004, Peoples R China.;[Liao, Maoxin] Univ South China, Sch Math & Phys, Hengyang 421001, Peoples R China.;[Li, Peiluan] Henan Univ Sci & Technol, Sch Math & Stat, Luoyang 471023, Peoples R China.;[Yuan, Shuai] Cent South Univ, Sch Math & Stat, Changsha 410083, Peoples R China.
通讯机构：
[Changjin Xu] G;Guizhou Key Laboratory of Economics System Simulation, Guizhou University of Finance and Economics, Guiyang 550004, PR China
关键词：
Complex-valued neural networks;Hopf bifurcation;Leakage delay;Stability;Fractional order
摘要：
During the past decades, integer-order complex-valued neural networks have attracted great attention since they have been widely applied in in many fields of engineering technology. However, the investigation on fractional-order complex-valued neural networks, which are more appropriate to characterize the dynamical nature of neural networks, is rare. In this manuscript, we are to consider the stability and the existence of Hopf bifurcation of fractional-order complex-valued neural networks. By separating the coefficients and the activation functions into their real and imaginary parts and choosing the time delay as bifurcation parameter, we establish a set of sufficient conditions to ensure the stability of the equilibrium point and the existence of Hopf bifurcation for the involved network. The study shows that both the fractional order and the leakage delay have an important impact on the stability and the existence of Hopf bifurcation of the considered model. Some suitable numerical simulations are implemented to illustrate the pivotal theoretical predictions. At last, we ends this article with a simple conclusion. (C) 2020 Elsevier Ltd. All rights reserved.
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Fractional-order bidirectional associate memory (BAM) neural networks with multiple delays: The case of Hopf bifurcation
作者：
Xu, Changjin* ;Liu, Zixin;Liao, Maoxin;Li, Peiluan;Xiao, Qimei;...
期刊：
Mathematics and Computers in Simulation ,2021年182:471-494 ISSN：0378-4754
通讯作者：
Xu, Changjin
作者机构：
[Xu, Changjin] Guizhou Univ Finance & Econ, Guizhou Key Lab Econ Syst Simulat, Guiyang 550004, Peoples R China.;[Liu, Zixin] Guizhou Univ Finance & Econ, Sch Math & Stat, Guiyang 550004, Peoples R China.;[Liao, Maoxin] Univ South China, Sch Math & Phys, Hengyang 421001, Peoples R China.;[Li, Peiluan] Henan Univ Sci & Technol, Sch Math & Stat, Luoyang 471023, Peoples R China.;[Xiao, Qimei] Changsha Univ Sci & Technol, Hunan Prov Key Lab Math Modeling & Anal Engn, Changsha 410114, Peoples R China.
通讯机构：
[Xu, Changjin] G;Guizhou Univ Finance & Econ, Guizhou Key Lab Econ Syst Simulat, Guiyang 550004, Peoples R China.
关键词：
Laplace transforms;Neural networks;Stability;BAM neural network;Critical value;Differential systems;Effect of parameters;Fractional order;Multiple delays;Stability theories;Vital effects;Hopf bifurcation
摘要：
The stability and Hopf bifurcation have important effect on the design of neural networks. By revealing the effect of parameters on the stability and Hopf bifurcation of neural networks, we can better apply neural networks to serve humanity. This article is principally concerned with the stability and the emergence of Hopf bifurcation of fractional-order BAM neural networks with multiple delays. Applying Laplace transform, stability theory and Hopf bifurcation knowledge of fractional-order differential systems, we establish a new sufficient condition to ensure the stability and the emergence of Hopf bifurcation of the addressed fractional-order BAM neural networks with multiple delays. The research indicates that the delay has a vital effect on the stability and the appearance of Hopf bifurcation of fractional-order BAM neural networks. Computer simulations are put into effect to test the effectiveness of the theoretical findings. It is shown that when the sum of time delays crosses some critical values, the stability of networks loses and Hopf bifurcation will happen. (C) 2020 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.
语种：
英文
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Anti-periodic Oscillations of Fuzzy Delayed Cellular Neural Networks with Impulse on Time Scales
作者：
Xu, Changjin* ;Liao, Maoxin;Li, Peiluan;Liu, Zixin
期刊：
Neural Processing Letters ,2020年51(3):2379-2402 ISSN：1370-4621
通讯作者：
Xu, Changjin
作者机构：
[Xu, Changjin] Guizhou Univ Finance & Econ, Guizhou Key Lab Econ Syst Simulat, Guiyang 550004, Peoples R China.;[Liao, Maoxin] Univ South China, Sch Math & Phys, Hengyang 421001, Peoples R China.;[Li, Peiluan] Henan Univ Sci & Technol, Sch Math & Stat, Luoyang 471023, Peoples R China.;[Liu, Zixin] Guizhou Univ Finance & Econ, Sch Math & Stat, Guiyang 550004, Peoples R China.
通讯机构：
[Xu, Changjin] G;Guizhou Univ Finance & Econ, Guizhou Key Lab Econ Syst Simulat, Guiyang 550004, Peoples R China.
关键词：
Asymptotic stability;Calculations;Fuzzy inference;Fuzzy neural networks;Lyapunov functions;Time measurement;Anti-periodic;Anti-periodic solutions;Delayed cellular neural networks;Impulse;Mathematical inequality;Sufficient criterion;Time scale calculus;Time-scales;Cellular neural networks
摘要：
In this manuscript, fuzzy delayed cellular neural networks with impulse are studied. Applying time scale calculus knowledge, mathematical inequalities and constructing Lyapunov function, we establish a sufficient criterion that guarantees the existence and exponential stability of anti-periodic solutions for fuzzy delayed cellular neural networks with impulse. In addition, an example with its numerical simulations is given to illustrate our theoretical predictions. © 2020, Springer Science+Business Media, LLC, part of Springer Nature.
语种：
英文
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Bifurcation analysis for a fractional-order chemotherapy model with two different delays
作者：
Xu, Changjin* ;Li, Peiluan;Liao, Maoxin;Yuan, Shuai
期刊：
Mathematical Methods in the Applied Sciences ,2020年43(3):1053-1083 ISSN：0170-4214
通讯作者：
Xu, Changjin
作者机构：
[Xu, Changjin] Guizhou Univ Finance & Econ, Guizhou Key Lab Econ Syst Simulat, Guiyang 550004, Guizhou, Peoples R China.;[Li, Peiluan] Henan Univ Sci & Technol, Sch Math & Stat, Luoyang 471023, Peoples R China.;[Liao, Maoxin] Univ South China, Sch Math & Phys, Hengyang 421001, Peoples R China.;[Yuan, Shuai] Cent South Univ, Sch Math & Stat, Changsha 410083, Hunan, Peoples R China.
通讯机构：
[Xu, Changjin] G;Guizhou Univ Finance & Econ, Guizhou Key Lab Econ Syst Simulat, Guiyang 550004, Guizhou, Peoples R China.
关键词：
Chemotherapy;Convergence of numerical methods;Differential equations;Diseases;MATLAB;Oncology;Stability criteria;Analytical predictions;Bifurcation analysis;delay;Dynamical properties;Fractional order;Fractional-order differential equations;Intrinsic characteristics;Stability theories;Hopf bifurcation
摘要：
Cancer is one of the most serious diseases in the world. The investigation on cancer treatment has attracted great attention from medical workers, mathematical researchers, and scholars in various fields. To understand the intrinsic characteristics of cancer, numerous scholars have established cancer treatment models and discussed the dynamical properties. However, the main work of many scholars only focuses on the integer-order cancer treatment models, while the study on fractional-order ones is quite a few. In the present article, on the basis of previous publications, we will put up a new fractional-order chemotherapy model with two different delays. By applying the stability theory and the Hopf bifurcation of fractional-order differential equations, we obtain a series of new stability criteria of the involved model and some sufficient conditions to ensure the existence of Hopf bifurcation of the involved model. Furthermore, the impact of two different delays and the fractional order on the stability and the emergence of Hopf bifurcation of involved model is presented. To illustrate the validity of analytical predictions, we perform computer simulations with Matlab software. The theoretical results in the manuscript are innovative and play an important role in cancer treatment. © 2019 John Wiley & Sons, Ltd.
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英文
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Antiperiodic solutions to delayed inertial quaternion-valued neural networks
作者：
Xu, Changjin* ;Li, Peiluan;Liao, Maoxin;Liu, Zixin;Xiao, Qimei
期刊：
Mathematical Methods in the Applied Sciences ,2020年43(12):7326-7344 ISSN：0170-4214
通讯作者：
Xu, Changjin
作者机构：
[Xu, Changjin] Guizhou Univ Finance & Econ, Guizhou Key Lab Econ Syst Simulat, Guiyang 550004, Peoples R China.;[Li, Peiluan] Henan Univ Sci & Technol, Sch Math & Stat, Luoyang 471023, Peoples R China.;[Liao, Maoxin] Univ South China, Sch Math & Phys, Hengyang 421001, Peoples R China.;[Liu, Zixin] Guizhou Univ Finance & Econ, Sch Math & Stat, Guiyang 550004, Peoples R China.;[Xiao, Qimei] Changsha Univ Sci & Technol, Hunan Prov Key Lab Math Modeling & Anal Engn, Changsha 410114, Peoples R China.
通讯机构：
[Xu, Changjin] G;Guizhou Univ Finance & Econ, Guizhou Key Lab Econ Syst Simulat, Guiyang 550004, Peoples R China.
关键词：
Engineering;Mathematical techniques;Anti-periodic solutions;Coincidence degree theory;Inertial terms;Sufficient criterion;Lyapunov functions
摘要：
This manuscript mainly deals with quaternion-valued neural networks (QVNNs) with delays and inertial term. Using Wirtinger inequality and coincidence degree theory, a new sufficient criterion to ensure the existence of antiperiodic solution of involved quaternion-valued neural networks is derived. With the aid of Lyapunov function, we discuss the exponential stability of antiperiodic solutions to quaternion-valued neural networks. Numerical simulations are presented to illustrate the established theoretical findings. © 2020 John Wiley & Sons, Ltd.
语种：
英文
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Chaos control strategy for a fractional-order financial model
作者：
Xu, Changjin* ;Aouiti, Chaouki;Liao, Maoxin* ;Li, Peiluan;Liu, Zixin
期刊：
Advances in Difference Equations ,2020年2020(1):1-17 ISSN：1687-1839
通讯作者：
Xu, Changjin;Liao, Maoxin
作者机构：
[Xu, Changjin] Guizhou Univ Finance & Econ, Guizhou Key Lab Econ Syst Simulat, Guiyang 550004, Peoples R China.;[Aouiti, Chaouki] Univ Carthage, Fac Sci Bizerte, UR13ES47 Res Units Math & Applicat, Bizerte, Tunisia.;[Liao, Maoxin] Univ South China, Sch Math & Phys, Hengyang 421001, Peoples R China.;[Li, Peiluan] Henan Univ Sci & Technol, Sch Math & Stat, Luoyang 471023, Peoples R China.;[Liu, Zixin] Guizhou Univ Finance & Econ, Sch Math & Stat, Guiyang 550004, Peoples R China.
通讯机构：
[Xu, Changjin] G;[Liao, Maoxin] U;Guizhou Univ Finance & Econ, Guizhou Key Lab Econ Syst Simulat, Guiyang 550004, Peoples R China.;Univ South China, Sch Math & Phys, Hengyang 421001, Peoples R China.
关键词：
Chaos control;Financial model;Stability;Hopf bifurcation;Fractional order;Delay
摘要：
In this paper, we propose a new fractional-order financial model which is a generalized version of the financial model reported in the previous publications. By applying a suitable time-delayed feedback controller, we have control for the chaotic behavior of the fractional-order financial model. We investigate the stability and the existence of a Hopf bifurcation of the fractional-order financial model. A new sufficient condition that guarantees the stability and the existence of a Hopf bifurcation for a fractional-order delayed financial model is presented by regarding the delay as bifurcation parameter. The investigation shows that the delay and the fractional order have an important effect on the stability and Hopf bifurcation of involved model. Some simulations justifying the validity of the derived analytical results are given. The obtained results of this article are innovative and are of great significance in handling the financial issues.
语种：
英文
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New insights on weighted pseudo almost periodic solutions in a Lasota-Wazewska system
作者：
Xu, Changjin* ;Liao, Maoxin;Li, Peiluan;Yuan, Shuai
期刊：
Advances in Difference Equations ,2020年2020(1):1-8 ISSN：1687-1839
通讯作者：
Xu, Changjin
作者机构：
[Xu, Changjin] Guizhou Univ Finance & Econ, Guizhou Key Lab Econ Syst Simulat, Guiyang, Peoples R China.;[Liao, Maoxin] Univ South China, Sch Math & Phys, Hengyang, Peoples R China.;[Li, Peiluan] Henan Univ Sci & Technol, Sch Math & Stat, Luoyang, Peoples R China.;[Yuan, Shuai] Cent South Univ, Sch Math & Stat, Changsha, Peoples R China.
通讯机构：
[Xu, Changjin] G;Guizhou Univ Finance & Econ, Guizhou Key Lab Econ Syst Simulat, Guiyang, Peoples R China.
关键词：
Global exponentially stability;Lasota–Wazewska system;Time delay;Weighted pseudo almost periodic solution
摘要：
<jats:title>Abstract</jats:title><jats:p>We study the weighted pseudo almost periodic solutions of a Lasota–Wazewska system. With the aid of fixed point theory and differential inequality strategies, we give a set of new sufficient criteria that guarantee the existence and global exponential stability of weighted pseudo almost periodic solutions to a Lasota–Wazewska system. The obtained results of this manuscript are completely innovative and complement the work of Shao (Appl. Math. Lett. 43:90–95, 2015) to some degree. So far, no scholars have investigated this aspect.</jats:p>
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英文
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Periodic Property and Asymptotic Behavior for a Discrete Ratio-Dependent Food-Chain System with Delays
作者：
Xu, Changjin* ;Li, Peiluan;Liao, Maoxin
期刊：
Discrete Dynamics in Nature and Society ,2020年2020:1-12 ISSN：1026-0226
通讯作者：
Xu, Changjin
作者机构：
[Xu, Changjin] Guizhou Univ Finance & Econ, Guizhou Key Lab Econ Syst Simulat, Guiyang 550004, Peoples R China.;[Li, Peiluan] Henan Univ Sci & Technol, Sch Math & Stat, Luoyang 471023, Peoples R China.;[Liao, Maoxin] Univ South China, Sch Math & Phys, Hengyang 421001, Peoples R China.
通讯机构：
[Xu, Changjin] G;Guizhou Univ Finance & Econ, Guizhou Key Lab Econ Syst Simulat, Guiyang 550004, Peoples R China.
摘要：
In this paper, a discrete ratio-dependent food-chain system with delay is investigated. By using Gaines and Mawhin's continuation theorem of coincidence degree theory and the method of Lyapunov function, a set of sufficient conditions for the existence of positive periodic solutions and global asymptotic stability of the model are established. © 2020 Changjin Xu et al.
语种：
英文
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Almost automorphic solutions to cellular neural networks with neutral type delays and leakage delays on time scales
作者：
Xu, Changjin* ;Liao, Maoxin;Li, Peiluan;Liu, Zixin
期刊：
International Journal of Computational Intelligence Systems ,2020年13(1):1-11 ISSN：1875-6891
通讯作者：
Xu, Changjin
作者机构：
[Xu, Changjin] Guizhou Univ Finance & Econ, Guizhou Key Lab Econ Syst Simulat, Guiyang 550004, Peoples R China.;[Liao, Maoxin] Univ South China, Sch Math & Phys, Hengyang 421001, Peoples R China.;[Li, Peiluan] Henan Univ Sci & Technol, Sch Math & Stat, Luoyang 471023, Peoples R China.;[Liu, Zixin] Guizhou Univ Finance & Econ, Sch Math & Stat, Guiyang 550004, Peoples R China.
通讯机构：
[Xu, Changjin] G;Guizhou Univ Finance & Econ, Guizhou Key Lab Econ Syst Simulat, Guiyang 550004, Peoples R China.
关键词：
Asymptotic stability;Calculations;Fixed point arithmetic;Time measurement;Almost automorphic;Fixed point theorems;Leakage delays;Linear dynamic equations;Neutral-type delay;Time varying;Time-scales;Cellular neural networks
摘要：
In this paper, cellular neural networks (CNNs) with neutral type delays and time-varying leakage delays are investigated. By applying the existence of the exponential dichotomy of linear dynamic equations on time scales, a fixed point theorem and the theory of calculus on time scales, a set of sufficient conditions which ensure the existence and exponential stability of almost automorphic solutions of the model are obtained. An example with its numerical simulations is given to support the theoretical findings. © 2020 The Authors. Published by Atlantis Press SARL.
语种：
英文
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New convergence results on cellular neural networks with leakage delay and proportional delay
作者：
Xu, Changjin* ;Liao, Maoxin;Li, Peiluan
期刊：
AIP Advances ,2020年10(7):075022 ISSN：2158-3226
通讯作者：
Xu, Changjin
作者机构：
[Xu, Changjin] Guizhou Univ Finance & Econ, Guizhou Key Lab Econ Syst Simulat, Guiyang 550004, Peoples R China.;[Liao, Maoxin] Univ South China, Sch Math & Phys, Hengyang 421001, Peoples R China.;[Li, Peiluan] Henan Univ Sci & Technol, Sch Math & Stat, Luoyang 471023, Peoples R China.
通讯机构：
[Xu, Changjin] G;Guizhou Univ Finance & Econ, Guizhou Key Lab Econ Syst Simulat, Guiyang 550004, Peoples R China.
摘要：
In the present work, we mainly focus on shunting inhibitory cellular neural networks (SICNNs) involving leakage delays and proportional delays. By applying the inequality technique, a novel sufficient criterion to ascertain the convergence of every solution of SICNNs with leakage delays and proportional delays is derived. Simulation results are delineated to substantiate the correctness of our theoretical findings. Up to now, very few scholars deal with the neural networks with leakage delays and proportional delays. The derived conclusion of this work is a novelty and supplements several earlier works. © 2020 Author(s).
语种：
英文
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Control Scheme for a Fractional-Order Chaotic Genesio-Tesi Model
作者：
Xu, Changjin* ;Li, Peiluan;Liao, Maoxin;Liu, Zixin;Xiao, Qimei;...
期刊：
Complexity ,2019年2019:4678394:1-4678394:15 ISSN：1076-2787
通讯作者：
Xu, Changjin
作者机构：
[Xu, Changjin] Guizhou Univ Finance & Econ, Guizhou Key Lab Econ Syst Simulat, Guiyang 550004, Guizhou, Peoples R China.;[Li, Peiluan] Henan Univ Sci & Technol, Sch Math & Stat, Luoyang 471023, Peoples R China.;[Liao, Maoxin] Univ South China, Sch Math & Phys, Hengyang 421001, Peoples R China.;[Liu, Zixin] Guizhou Univ Finance & Econ, Sch Math & Stat, Guiyang 550004, Guizhou, Peoples R China.;[Xiao, Qimei] Changsha Univ Sci & Technol, Hunan Prov Key Lab Math Modeling & Anal Engn, Changsha 410114, Hunan, Peoples R China.
通讯机构：
[Xu, Changjin] G;Guizhou Univ Finance & Econ, Guizhou Key Lab Econ Syst Simulat, Guiyang 550004, Guizhou, Peoples R China.
摘要：
In this paper, based on the earlier research, a new fractional-order chaotic Genesio-Tesi model is established. The chaotic phenomenon of the fractional-order chaotic Genesio-Tesi model is controlled by designing two suitable time-delayed feedback controllers. With the aid of Laplace transform, we obtain the characteristic equation of the controlled chaotic Genesio-Tesi model. Then by regarding the time delay as the bifurcation parameter and analyzing the characteristic equation, some new sufficient criteria to guarantee the stability and the existence of Hopf bifurcation for the controlled fractional-order chaotic Genesio-Tesi model are derived. The research shows that when time delay remains in some interval, the equilibrium point of the controlled chaotic Genesio-Tesi model is stable and a Hopf bifurcation will happen when the time delay crosses a critical value. The effect of the time delay on the stability and the existence of Hopf bifurcation for the controlled fractional-order chaotic Genesio-Tesi model is shown. At last, computer simulations check the rationalization of the obtained theoretical prediction. The derived key results in this paper play an important role in controlling the chaotic behavior of many other differential chaotic systems. © 2019 Changjin Xu et al.
语种：
英文
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Bifurcation Analysis for Simplified Five-Neuron Bidirectional Associative Memory Neural Networks with Four Delays
作者：
Xu, Changjin* ;Liao, Maoxin;Li, Peiluan;Guo, Ying
期刊：
Neural Processing Letters ,2019年50(3):2219-2245 ISSN：1370-4621
通讯作者：
Xu, Changjin
作者机构：
[Xu, Changjin] Guizhou Univ Finance & Econ, Guizhou Key Lab Econ Syst Simulat, Guiyang 550004, Guizhou, Peoples R China.;[Liao, Maoxin] Univ South China, Sch Math & Phys, Hengyang 421001, Peoples R China.;[Li, Peiluan] Henan Univ Sci & Technol, Sch Math & Stat, Luoyang 471023, Peoples R China.;[Guo, Ying] Cent S Univ, Sch Informat Sci & Engn, Changsha 410083, Hunan, Peoples R China.
通讯机构：
[Xu, Changjin] G;Guizhou Univ Finance & Econ, Guizhou Key Lab Econ Syst Simulat, Guiyang 550004, Guizhou, Peoples R China.
关键词：
Associative processing;Associative storage;Convergence of numerical methods;Memory architecture;Neural networks;Stability;Time delay;BAM neural network;Bi-directional associative memory neural networks;Bifurcation analysis;Center manifold theory;Hopf bifurcation theory;Normal form theory;Stability and bifurcation analysis;Transcendental equations;Hopf bifurcation
摘要：
The paper deals with the stability and bifurcation analysis of a class of simplified five-neuron bidirectional associative memory neural networks with four delays. By discussing the characteristic transcendental equation and applying Hopf bifurcation theory, some sufficient conditions which guarantee the local stability and the existence of Hopf bifurcation of the neural networks are established. With the aid of the normal form theory and center manifold theory, we obtain some specific formulae to determine the stability and the direction of the Hopf bifurcation. Computer simulations are implemented to explain the key mathematical predictions. The paper ends with a brief conclusion. © 2019, Springer Science+Business Media, LLC, part of Springer Nature.
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英文
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PD9 Control Strategy for a Fractional-Order Chaotic Financial Model
作者：
Xu, Changjin* ;Liao, Maoxin;Li, Peiluan;Xiao, Qimei;Yuan, Shuai
期刊：
Complexity ,2019年2019:2989204:1-2989204:14 ISSN：1076-2787
通讯作者：
Xu, Changjin
作者机构：
[Xu, Changjin] Guizhou Univ Finance & Econ, Guizhou Key Lab Econ Syst Simulat, Guiyang 550004, Guizhou, Peoples R China.;[Liao, Maoxin] Univ South China, Sch Math & Phys, Hengyang 421001, Peoples R China.;[Li, Peiluan] Henan Univ Sci & Technol, Sch Math & Stat, Luoyang 471023, Peoples R China.;[Xiao, Qimei] Changsha Univ Sci & Technol, Hunan Prov Key Lab Math Modeling & Anal Engn, Changsha 410114, Hunan, Peoples R China.;[Yuan, Shuai] Cent S Univ, Sch Math & Stat, Changsha 410083, Hunan, Peoples R China.
通讯机构：
[Xu, Changjin] G;Guizhou Univ Finance & Econ, Guizhou Key Lab Econ Syst Simulat, Guiyang 550004, Guizhou, Peoples R China.
摘要：
In this article, based on the previous works, a new fractional-order financial model is put up. The chaotic behavior of the fractional-order financial model is suppressed by designing an appropriate PD9 controller. By choosing the delay as the bifurcation parameter, we establish the sufficient condition to guarantee the stability and the existence of Hopf bifurcation of fractional-order financial model. Also, the influence of the delay and the fractional order on the stability and the existence of Hopf bifurcation of fractional-order financial model is revealed. An example is given to confirm the effectiveness of the analysis results. The main findings of this article play an important role in maintaining economic stability. © 2019 Changjin Xu et al.
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英文
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A new method to investigate almost periodic solutions for an Nicholson's blowflies model with time-varying delays and a linear harvesting term
作者：
Xu, Changjin* ;Liao, Maoxin;Li, Peiluan;Xiao, Qimei;Yuan, Shuai
期刊：
MATHEMATICAL BIOSCIENCES AND ENGINEERING ,2019年16(5):3830-3840 ISSN：1547-1063
通讯作者：
Xu, Changjin
作者机构：
[Xu, Changjin] Guizhou Univ Finance & Econ, Guizhou Key Lab Econ Syst Simulat, Guiyang 550004, Guizhou, Peoples R China;[Liao, Maoxin] Univ South China, Sch Math & Phys, Hengyang 421001, Peoples R China;[Li, Peiluan] Henan Univ Sci & Technol, Sch Math & Stat, Luoyang 471023, Peoples R China;[Xiao, Qimei] Changsha Univ Sci & Technol, Hunan Prov Key Lab Math Modeling & Anal Engn, Changsha 410114, Hunan, Peoples R China;[Yuan, Shuai] Cent S Univ, Sch Math & Stat, Changsha 410083, Hunan, Peoples R China
通讯机构：
[Xu, Changjin] G;Guizhou Univ Finance & Econ, Guizhou Key Lab Econ Syst Simulat, Guiyang 550004, Guizhou, Peoples R China.
关键词：
Fixed point arithmetic;Integral equations;Time delay;Almost periodic solutions;Exponential dichotomy;Fixed point theorem in cones;Linear harvesting terms;Nicholson's Blowflies models;Positive almost periodic solutions;Time varying- delays;Human computer interaction;algorithm;animal;biological model;computer simulation;Diptera;female;nonlinear system;ovum;physiology;population dynamics;reproduction;signal processing;statistical model;time factor;Algorithms;Animals;Computer Simulation;Diptera;Female;Linear Models;Models, Biological;Nonlinear Dynamics;Ovum;Population Dynamics;Reproduction;Signal Processing, Computer-Assisted;Time Factors
摘要：
In this paper, a delayed Nicholson's blowflies model with a linear harvesting term is investigated. By transforming the model into an equivalent integral equation, and applying a fixed point theorem in cones, we establish a sufficient condition which ensure the existence of positive almost periodic solutions for the Nicholson's blowflies model. The results of this paper are completely new and complement those of the previous studies. The approach is new.
语种：
英文
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Bifurcation of a Fractional-Order Delayed Malware Propagation Model in Social Networks
作者：
Xu, Changjin* ;Liao, Maoxin;Li, Peiluan
期刊：
Discrete Dynamics in Nature and Society ,2019年2019(Pt.1):7057052-1-7057052-10 ISSN：1026-0226
通讯作者：
Xu, Changjin
作者机构：
[Xu, Changjin] Guizhou Univ Finance & Econ, Guizhou Key Lab Econ Syst Simulat, Guiyang 550004, Guizhou, Peoples R China.;[Liao, Maoxin] Univ South China, Sch Math & Phys, Hengyang 421001, Peoples R China.;[Li, Peiluan] Henan Univ Sci & Technol, Sch Math & Stat, Luoyang 471023, Peoples R China.
通讯机构：
[Xu, Changjin] G;Guizhou Univ Finance & Econ, Guizhou Key Lab Econ Syst Simulat, Guiyang 550004, Guizhou, Peoples R China.
关键词：
Bifurcation;Fractional-Order Delayed;Malware Propagation
摘要：
In recent years, with the rapid development of the Internet and the Internet of Things, network security is urgently needed. Malware becomes a major threat to network security. Thus, the study on malware propagation model plays an important role in network security. In the past few decades, numerous researchers put up various kinds of malware propagation models to analyze the dynamic interaction. However, many works are only concerned with the integer-order malware propagation models, while the investigation on fractional-order ones is very few. In this paper, based on the earlier works, we will put up a new fractional-order delayed malware propagation model. Letting the delay be bifurcation parameter and analyzing the corresponding characteristic equations of considered system, we will establish a set of new sufficient conditions to guarantee the stability and the existence of Hopf bifurcation of fractional-order delayed malware propagation model. The study shows that the delay and the fractional order have important effect on the stability and Hopf bifurcation of considered system. To check the correctness of theoretical analyses, we carry out some computer simulations. At last, a simple conclusion is drawn. The derived results of this paper are completely innovative and play an important guiding role in network security. © 2019 Changjin Xu et al.
语种：
英文
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Bifurcation control for a fractional-order competition model of Internet with delays
作者：
Xu, Changjin* ;Liao, Maoxin;Li, Peiluan
期刊：
Nonlinear Dynamics ,2019年95(4):3335-3356 ISSN：0924-090X
通讯作者：
Xu, Changjin
作者机构：
[Xu, Changjin] Guizhou Univ Finance & Econ, Guizhou Key Lab Econ Syst Simulat, Guiyang 550004, Peoples R China.;[Liao, Maoxin] Univ South China, Sch Math & Phys, Hengyang 421001, Peoples R China.;[Li, Peiluan] Henan Univ Sci & Technol, Sch Math & Stat, Luoyang 471023, Peoples R China.
通讯机构：
[Xu, Changjin] G;Guizhou Univ Finance & Econ, Guizhou Key Lab Econ Syst Simulat, Guiyang 550004, Peoples R China.
关键词：
Bifurcation control;Competitive web site model;Internet;Stability;Hopf bifurcation;Fractional order;Delay
摘要：
In today’s society, the Internet has become an important tool of our life due to its potential applications in various areas such as economics, industry, agriculture, medical and health care, and information processing. To understand and grasp the law of the Internet, many competitive web site models of the Internet and some phenomena related to World Wide Web have been investigated systematically. However, many scholars only study the integer-order competitive web site models of the Internet. Up to now, there are few papers that focus on the dynamics of fractional-order competitive web site models of Internet, which possess memory property. In this paper, we are concerned with the stability and the existence of Hopf bifurcation of a fractional-order competitive web site model of Internet. By choosing the time delay as parameter and applying the Routh–Hurwitz criteria, we will establish a new sufficient condition guaranteeing the stability and the existence of Hopf bifurcation for fractional-order competitive web site model of Internet. The research reveals that fractional order and the delay play a key role in describing the stability and Hopf bifurcation of the considered system. Computer simulations are implemented to support the analytic results. Finally, a simple conclusion is presented. The theoretical findings of this article have a great significance in handling the competition dynamics among different web sites. © 2019, Springer Nature B.V.
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英文
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